Compare the light gathering power of a telescope with a 10-centimeter(about 4-inch) diameter mirror to that of the human eye. (Take a diameter of the pupil of the eye to be about 5 millimeters)

To compare the light gathering power of a telescope with a 10-centimeter diameter mirror to that of the human eye, we need to calculate the surface area of each in order to determine how much light they can collect.

Here's how you can calculate the light gathering power:

1. Calculate the surface area of the telescope mirror:
- The formula for the surface area of a circle is A = πr², where A is the surface area and r is the radius.
- The radius of the telescope mirror is half its diameter, so it would be 5 centimeters (or 0.05 meters).
- Substitute the values into the formula: A = π(0.05)²
- Calculate the surface area: A ≈ 0.00785 square meters.

2. Calculate the surface area of the human eye's pupil:
- The formula for the surface area of a circle is again A = πr², where A is the surface area and r is the radius.
- The radius of the human eye's pupil is half its diameter, so it would be 0.0025 meters (or 2.5 millimeters).
- Substitute the values into the formula: A = π(0.0025)²
- Calculate the surface area: A ≈ 0.00001963 square meters.

3. Compare the surface areas:
- Divide the surface area of the telescope mirror by the surface area of the human eye's pupil:
0.00785 / 0.00001963 ≈ 399.

The result indicates that the telescope with a 10-centimeter diameter mirror has a light gathering power approximately 399 times greater than that of the human eye.